In this paper, we introduce a simple formula for conditional Wiener integrals over C0(𝔹), the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on C0(𝔹) in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral...

In these notes, conjectures about the exact semi-classical expansion of eigenvalues of
hamiltonians corresponding to potentials with degenerate minima, are recalled. They were
initially motivated by semi-classical calculations of quantum partition functions using a
path integral representation and have later been proven to a large extent, using the
theory of resurgent functions. They take the form of generalized Bohr--Sommerfeld
quantization formulae. We explain here their...